01 - Pat chicken breasts dry with paper towels. Season both sides generously with salt and black pepper. Dredge each breast lightly in flour, shaking off excess.
02 - Heat olive oil and butter in a large skillet over medium-high heat until butter foams. Add chicken breasts and sear for 4 to 5 minutes per side until golden brown and cooked through. Transfer to a plate and cover loosely with foil.
03 - Reduce heat to medium. Add minced garlic to the same skillet and sauté for 1 minute until fragrant, being careful not to burn.
04 - Pour in chicken broth, using a wooden spoon to scrape up browned bits from the bottom of the skillet. Let simmer for 2 minutes to reduce slightly.
05 - Stir in heavy cream, lemon zest, and lemon juice. Bring to a gentle simmer. Whisk in grated Parmesan cheese until fully melted and sauce thickens slightly, about 2 to 3 minutes.
06 - Return chicken breasts to the skillet, spooning sauce generously over each piece. Simmer for 3 to 4 minutes until chicken is heated through.
07 - Sprinkle with chopped fresh parsley and crushed red pepper flakes if desired. Serve immediately with additional Parmesan and parsley for garnish.